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001 978-3-642-38206-2
003 DE-He213
005 20190213151904.0
007 cr nn 008mamaa
008 130822s2013 gw | s |||| 0|eng d
020 _a9783642382062
_9978-3-642-38206-2
024 7 _a10.1007/978-3-642-38206-2
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aHarima, Tadahito.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Lefschetz Properties
_h[electronic resource] /
_cby Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXIX, 250 p. 20 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2080
505 0 _aIntroduction and Historical Note -- 1. Poset Theory -- 2. Basics on the Theory of Local Rings -- 3. Lefschetz Properties -- 4. Compete Intersections with the SLP -- 5. A Generalization of Lefschetz Elements -- 6. k-Lefschetz Properties -- 7. Cohomology Rings -- 8.  Invariant Theory and Lefschetz Property -- 9. The Strong Lefschetz Property and the Schur–Weyl Duality.  .
520 _aThis is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically.
650 0 _aAlgebra.
650 0 _aGeometry, algebraic.
650 0 _aCombinatorics.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aCombinatorics.
_0http://scigraph.springernature.com/things/product-market-codes/M29010
700 1 _aMaeno, Toshiaki.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aMorita, Hideaki.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aNumata, Yasuhide.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aWachi, Akihito.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aWatanabe, Junzo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642382055
776 0 8 _iPrinted edition:
_z9783642382079
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2080
856 4 0 _uhttps://doi.org/10.1007/978-3-642-38206-2
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c12233
_d12233